Problem: Solve for $x$ and $y$ using elimination. ${x-5y = -35}$ ${4x-3y = -4}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ ${-4x+20y = 140}$ $4x-3y = -4$ Add the top and bottom equations together. $17y = 136$ $\dfrac{17y}{{17}} = \dfrac{136}{{17}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {x-5y = -35}\thinspace$ to find $x$ ${x - 5}{(8)}{= -35}$ $x-40 = -35$ $x-40{+40} = -35{+40}$ ${x = 5}$ You can also plug ${y = 8}$ into $\thinspace {4x-3y = -4}\thinspace$ and get the same answer for $x$ : ${4x - 3}{(8)}{= -4}$ ${x = 5}$